Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories.

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Early Evolutionary Selection of NAD Biosynthesis Pathway in Bacteria.

Bacteria use two alternative pathways to synthesize nicotinamide adenine dinucleotide (NAD) from nicotinamide (Nam). A short, two-step route proceeds through nicotinamide mononucleotide (NMN) formation, whereas the other pathway, a four-step route, includes the deamidation of Nam and the reamidation of nicotinic acid adenine dinucleotide (NAAD) to NAD. In addition to having twice as many enzymatic steps, the four-step route appears energetically unfavourable, because the amidation of NAAD includes the cleavage of ATP to AMP. Therefore, it is surprising that this pathway is prevalent not only in bacteria but also in yeast and plants. Here, we demonstrate that the considerably higher chemical stability of the deamidated intermediates, compared with their amidated counterparts, might compensate for the additional energy expenditure, at least at elevated temperatures. Moreover, comprehensive bioinformatics analyses of the available >6000 bacterial genomes indicate that an early selection of one or the other pathway occurred. The mathematical modelling of the NAD pathway dynamics supports this hypothesis, as there appear to be no advantages in having both pathways.

[Formula: see text]: ComplexOme-Structural Network Interpreter used to study spatial enrichment in metazoan ribosomes.

BACKGROUND: Upon environmental stimuli, ribosomes are surmised to undergo compositional rearrangements due to abundance changes among proteins assembled into the complex, leading to modulated structural and functional characteristics. Here, we present the ComplexOme-Structural Network Interpreter ([Formula: see text]), a computational method to allow testing whether ribosomal proteins (rProteins) that exhibit abundance changes under specific conditions are spatially confined to particular regions within the large ribosomal complex. RESULTS: [Formula: see text] translates experimentally determined structures into graphs, with nodes representing proteins and edges the spatial proximity between them. In its first implementation, [Formula: see text] considers rProteins and ignores rRNA and other objects. Spatial regions are defined using a random walk with restart methodology, followed by a procedure to obtain a minimum set of regions that cover all proteins in the complex. Structural coherence is achieved by applying weights to the edges reflecting the physical proximity between purportedly contacting proteins. The weighting probabilistically guides the random-walk path trajectory. Parameter tuning during region selection provides the option to tailor the method to specific biological questions by yielding regions of different sizes with minimum overlaps. In addition, other graph community detection algorithms may be used for the [Formula: see text] workflow, considering that they yield different sized, non-overlapping regions. All tested algorithms result in the same node kernels under equivalent regions. Based on the defined regions, available abundance change information of proteins is mapped onto the graph and subsequently tested for enrichment in any of the defined spatial regions. We applied [Formula: see text] to the cytosolic ribosome structures of Saccharomyces cerevisiae, Oryctolagus cuniculus, and Triticum aestivum using datasets with available quantitative protein abundance change information. We found that in yeast, substoichiometric rProteins depleted from translating polysomes are significantly constrained to a ribosomal region close to the tRNA entry and exit sites. CONCLUSIONS: [Formula: see text] offers a computational method to partition multi-protein complexes into structural regions and a statistical approach to test for spatial enrichments of any given subsets of proteins. [Formula: see text] is applicable to any multi-protein complex given appropriate structural and abundance-change data. [Formula: see text] is publicly available as a GitHub repository https://github.com/MSeidelFed/COSNet_i and can be installed using the python installer pip.

Spatially Enriched Paralog Rearrangements Argue Functionally Diverse Ribosomes Arise during Cold Acclimation in Arabidopsis.

Ribosome biogenesis is essential for plants to successfully acclimate to low temperature. Without dedicated steps supervising the 60S large subunits (LSUs) maturation in the cytosol, e.g., Rei-like (REIL) factors, plants fail to accumulate dry weight and fail to grow at suboptimal low temperatures. Around REIL, the final 60S cytosolic maturation steps include proofreading and assembly of functional ribosomal centers such as the polypeptide exit tunnel and the P-Stalk, respectively. In consequence, these ribosomal substructures and their assembly, especially during low temperatures, might be changed and provoke the need for dedicated quality controls. To test this, we blocked ribosome maturation during cold acclimation using two independent reil double mutant genotypes and tested changes in their ribosomal proteomes. Additionally, we normalized our mutant datasets using as a blank the cold responsiveness of a wild-type Arabidopsis genotype. This allowed us to neglect any reil-specific effects that may happen due to the presence or absence of the factor during LSU cytosolic maturation, thus allowing us to test for cold-induced changes that happen in the early nucleolar biogenesis. As a result, we report that cold acclimation triggers a reprogramming in the structural ribosomal proteome. The reprogramming alters the abundance of specific RP families and/or paralogs in non-translational LSU and translational polysome fractions, a phenomenon known as substoichiometry. Next, we tested whether the cold-substoichiometry was spatially confined to specific regions of the complex. In terms of RP proteoforms, we report that remodeling of ribosomes after a cold stimulus is significantly constrained to the polypeptide exit tunnel (PET), i.e., REIL factor binding and functional site. In terms of RP transcripts, cold acclimation induces changes in RP families or paralogs that are significantly constrained to the P-Stalk and the ribosomal head. The three modulated substructures represent possible targets of mechanisms that may constrain translation by controlled ribosome heterogeneity. We propose that non-random ribosome heterogeneity controlled by specialized biogenesis mechanisms may contribute to a preferential or ultimately even rigorous selection of transcripts needed for rapid proteome shifts and successful acclimation.

Systematic Review of Plant Ribosome Heterogeneity and Specialization.

Plants dedicate a high amount of energy and resources to the production of ribosomes. Historically, these multi-protein ribosome complexes have been considered static protein synthesis machines that are not subject to extensive regulation but only read mRNA and produce polypeptides accordingly. New and increasing evidence across various model organisms demonstrated the heterogeneous nature of ribosomes. This heterogeneity can constitute specialized ribosomes that regulate mRNA translation and control protein synthesis. A prominent example of ribosome heterogeneity is seen in the model plant, Arabidopsis thaliana, which, due to genome duplications, has multiple paralogs of each ribosomal protein (RP) gene. We support the notion of plant evolution directing high RP paralog divergence toward functional heterogeneity, underpinned in part by a vast resource of ribosome mutants that suggest specialization extends beyond the pleiotropic effects of single structural RPs or RP paralogs. Thus, Arabidopsis is a highly suitable model to study this phenomenon. Arabidopsis enables reverse genetics approaches that could provide evidence of ribosome specialization. In this review, we critically assess evidence of plant ribosome specialization and highlight steps along ribosome biogenesis in which heterogeneity may arise, filling the knowledge gaps in plant science by providing advanced insights from the human or yeast fields. We propose a data analysis pipeline that infers the heterogeneity of ribosome complexes and deviations from canonical structural compositions linked to stress events. This analysis pipeline can be extrapolated and enhanced by combination with other high-throughput methodologies, such as proteomics. Technologies, such as kinetic mass spectrometry and ribosome profiling, will be necessary to resolve the temporal and spatial aspects of translational regulation while the functional features of ribosomal subpopulations will become clear with the combination of reverse genetics and systems biology approaches.

From patterned response dependency to structured covariate dependency: Entropy based categorical-pattern-matching.

Data generated from a system of interest typically consists of measurements on many covariate features and possibly multiple response features across all subjects in a designated ensemble. Such data is naturally represented by one response-matrix against one covariate-matrix. A matrix lattice is an advantageous platform for simultaneously accommodating heterogeneous data types: continuous, discrete and categorical, and exploring hidden dependency among/between features and subjects. After each feature being individually renormalized with respect to its own histogram, the categorical version of mutual conditional entropy is evaluated for all pairs of response and covariate features according to the combinatorial information theory. Then, by applying Data Could Geometry (DCG) algorithmic computations on such a mutual conditional entropy matrix, multiple synergistic feature-groups are partitioned. Distinct synergistic feature-groups embrace distinct structures of dependency. The explicit details of dependency among members of synergistic features are seen through mutliscale compositions of blocks computed by a computing paradigm called Data Mechanics. We then propose a categorical pattern matching approach to establish a directed associative linkage: from the patterned response dependency to serial structured covariate dependency. The graphic display of such a directed associative linkage is termed an information flow and the degrees of association are evaluated via tree-to-tree mutual conditional entropy. This new universal way of discovering system knowledge is illustrated through five data sets. In each case, the emergent visible heterogeneity is an organization of discovered knowledge.

Comparative Normal Mode Analysis of the Dynamics of DENV and ZIKV Capsids.

Key steps in the life cycle of a virus, such as the fusion event as the virus infects a host cell and its maturation process, relate to an intricate interplay between the structure and the dynamics of its constituent proteins, especially those that define its capsid, much akin to an envelope that protects its genomic material. We present a comprehensive, comparative analysis of such interplay for the capsids of two viruses from the flaviviridae family, Dengue (DENV) and Zika (ZIKV). We use for that purpose our own software suite, DD-NMA, which is based on normal mode analysis. We describe the elements of DD-NMA that are relevant to the analysis of large systems, such as virus capsids. In particular, we introduce our implementation of simplified elastic networks and justify their parametrization. Using DD-NMA, we illustrate the importance of packing interactions within the virus capsids on the dynamics of the E proteins of DENV and ZIKV. We identify differences between the computed atomic fluctuations of the E proteins in DENV and ZIKV and relate those differences to changes observed in their high resolution structures. We conclude with a discussion on additional analyses that are needed to fully characterize the dynamics of the two viruses.

Lewis Carroll's Doublets net of English words: network heterogeneity in a complex system.

Lewis Carroll's English word game Doublets is represented as a system of networks with each node being an English word and each connectivity edge confirming that its two ending words are equal in letter length, but different by exactly one letter. We show that this system, which we call the Doublets net, constitutes a complex body of linguistic knowledge concerning English word structure that has computable multiscale features. Distributed morphological, phonological and orthographic constraints and the language's local redundancy are seen at the node level. Phonological communities are seen at the network level. And a balancing act between the language's global efficiency and redundancy is seen at the system level. We develop a new measure of intrinsic node-to-node distance and a computational algorithm, called community geometry, which reveal the implicit multiscale structure within binary networks. Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.